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This paper investigates the passivity-based sliding mode control (SMC) of switched stochastic singular systems under asynchronous switching. An integral-type sliding surface is designed. The asynchronous switching makes the entire time interval divided into matched periods and mismatched periods. Sufficient conditions for mean-square exponential stability and stochastic passivity of switched stochastic singular system are developed for a class of switching signals with average dwell time. The passification criterions are then established. Moreover, a SMC law is synthesized to ensure the reachability of sliding surface for corresponding subsystems in matched periods and mismatched periods.